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Write an explicit formula that represents the sequence defined by the following recursive formula: a_(1)=8" and "a_(n)=3a_(n-1) Answer: a_(n)=

Write an explicit formula that represents the sequence defined by the following recursive formula:\newlinea1=8 and an=3an−1 a_{1}=8 \text { and } a_{n}=3 a_{n-1} \newlineAnswer: an= a_{n}=

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Q. Write an explicit formula that represents the sequence defined by the following recursive formula:\newlinea1=8 and an=3an−1 a_{1}=8 \text { and } a_{n}=3 a_{n-1} \newlineAnswer: an= a_{n}=
  1. Identify Recursive Formula: The given recursive formula is a1=8a_{1}=8 and an=3an−1a_{n}=3a_{n-1}. This indicates that each term is three times the previous term, which suggests that the sequence is geometric.
  2. Use Geometric Sequence Formula: For a geometric sequence, the nth term is given by the formula an=a1×r(n−1)a_{n} = a_{1} \times r^{(n-1)}, where a1a_{1} is the first term and rr is the common ratio.
  3. Determine First Term and Ratio: We know the first term a1=8a_{1} = 8 and the common ratio r=3r = 3 (since each term is three times the previous term).
  4. Substitute Values into Formula: Substitute the values of a1a_{1} and rr into the formula for the nnth term of a geometric sequence to get the explicit formula.\newlinean=8×3(n−1)a_{n} = 8 \times 3^{(n-1)}

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